Answer
$N (E) = CE^{1/2}$
Work Step by Step
The original equation of Density of States (Conduction of electron in metal)
$N(E) = \frac{8\sqrt 2 \pi m^{3/2}}{h^3} E^{1/2} $
Since c is just constants, it can be written $N (E) = CE^{1/2}$
Additional info :
$C = \frac{8\sqrt 2 \pi (9.109\times 10^{-31} kg)^{3/2}}{(6.626\times 10^{-34} J.s)^3}$
$C = 1.062 \times 10^{56} kg^{3/2}/J^3.s^3$
